I'm reading Wheelock on kindle and making notes in Notepad. My usual keyboard and ASCII characters are kind of limited when it comes to words with certain characters. I have been sort of making do with what is available to me, like this:

I'm not absolutely certain, but it seems logical to me that the non negates the word nearest it. Therefore, when I read "nōn mē dēbēs laudāre" I take it to mean "it is not I whom you ought to praise"; when I read "nōn dēbēs mē laudāre" I take it to mean "you need not praise me," etc.

Remember that non is an adverb, that is, it will modify verbs, not nouns/pronouns. Staying within the bounds of chapter one, Wheelock points out that subject-object-verb is the common pattern. Using this the main verb of the sentence is clearly 'debes' (as it contains our subject) and thus should be at the end of the sentence. Objects will be before verbs so we can place 'me' at the start of the sentence. As for the placement of the 'non' and 'laudare', to avoid confusion the 'non' it should be placed before 'laudare'. If we reversed the order it could be read as either "You ought not to praise me" or as "You not ought (shouldn't) praise me." Really, the same meaning, but not the same sentence.

Edit: I realize I may accidentally send some students astray: it is true that adverbs will not modify nouns/pronouns, but they do modify more than just verbs (e.g. other adverbs, adjectives...); so keep that in mind!

I'm slightly confused by the above answer. I would have argued that laudāre is the main verb because it carries the main meaning of the sentence and it would not be complete without it. Secondly there are several examples from the Latin - English sentences in the Exercises at the back of the book:

Caput I Exercises:

10) 'Dēbēs monēre mē'You ought to warn me

11) 'Dēbētis servāre mē'You ought to save me.

12) 'Nōn dēbent laudāre mē'They ought not to praise me.

There are a few others but it's the last one which I took as an example for this sentence which I translated as 'nōn dēbes laudāre mē'.

debes/debetis is the main verb -- it's the verb that carries the inflexional endings. Tu/vos is the subject; the infinitive laudare is the complement of debes/debetis. The sentence is a statement about what tu/vos ought to do.

Latin word order is not as fixed as English; the default word order would be non debes me laudare, but you could move non around to any position in the sentence except the last. The meaning would change slightly, depending on which element you want to emphasize: